1. Field of the Invention
The present invention relates generally to data coding. In particular, the present invention relates to a method and apparatus for generating a low-density parity check (LDPC) code.
2. Description of the Related Art
In general, communication systems encode transmission data prior to transmission to increase transmission stability, avoiding retransmissions and increasing transmission efficiency. For this purpose, they use convolutional coding, turbo coding, etc.
The rapid development of wireless communication technology has driven the appearance of wireless communication systems that can transmit data at very high rates. For higher-rate data transmission, they need coding techniques that offer higher efficiency than the above existing coding methods.
In this context, LDPC codes have emerged as a promising coding method. The LDPC codes were first proposed by Gallager in the early 1960's and re-discovered by MacKay after the 1990's. MacKay's LDPC code is based on decoding using the sum-product algorithm. Using belief propagation, these LDPC codes have attracted attention as a code having excellent performance that approaches the Shannon capacity limit.
Richardson and Chung et al. later proposed density evolution. The basic idea of the density evolution is to track the probability distributions of messages generated and updated during decoding, which change according to the number of iterations, on a factor graph describing a LDPC code. Under the assumption of the density evolution and infinite iterations on the factor graph, a channel parameter was detected which converges the probability of error to “0”. That is, the degree distributions of variable nodes and check nodes, which maximize the channel parameter on the factor graph, were proposed. They theoretically demonstrated that this case is also applicable to LDPC codes of a finite length with cycles. With this density evolution technique, the channel capacity of irregular LDPC codes approaches to within 0.0045 dB of the theoretical Shannon limit.
These LDPC codes are discussed as a prominent alternative to turbo codes for future-generation mobile communication systems. This is because the LDPC codes have parallel structure and low complexity in the design of a decoder, low error-floor performance, and good frame error rate. Accordingly, it is expected that excellent LDPC codes will be proposed with more developmental efforts over the coming years.
Distinctive shortcomings with conventional LDPC codes, however, are greater complexity in terms of coding relative to turbo coding, difficulty in deciding an optimum code structure that offers better performance than turbo codes, for a short frame size, and require a large memory for LDPC code representation. Therefore, a need exists for an efficient LDPC code having flexibility in frame length.